# Goniomentry and trigonometry - examples - page 13

1. Apples
School kitchen bought 36kg apples for 12 kc/kg. How many kilograms of apples 1/4 cheaper can they buy for the same money?
2. Angle of diagonal
Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
3. Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
4. Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
5. Electric energy
There are 875 identical light bulbs in the sports hall lighting for 2 hours. How long does the same amount of electricity consume 100 such bulbs?
6. A map
A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions?
7. Inlet and outlet
The pool has a capacity of 50 hl. The inlet pipe flows in 1 minute 1.25 hl, and the waste pipe outlet is draining the full pool in 50 minutes. How long will take the empty the full pool when both the inlet and outlet are opened at the same time?
8. Five inlets
The tank can be filled with five equally powerful inlets. If the tank is filled by four of these inlets, it takes a total of 30 minutes to fill one-third of the tank. How many minutes does it take to fill an empty tank if it is filled with all five inlets?
9. The pond
We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
10. Right triangle
Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
11. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
12. Sugar production
From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?
13. Bicycle gear
The pedal bicycle wheel has 56 teeth and a rear 20 gear tooth. How many times does the bicycle wheel turn when you make 20 turns of the pedal wheel?
14. Children playground
The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
15. Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
16. Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees
17. Sixty
Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?
18. Tank 11
When 150 litres has been drawn from a tank it is 3/8 full, how many litres will the tank hold?
19. Diagonals of the rhombus
How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
20. Deviation of the lines
Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.